Some Problems and Results in Additive Combinatorics.

Additive combinatorics is a relatively new field, with
many diverse and exciting research programmes. In this talk I will discuss
two of these programmes -- the continuing development of
sum-product inequalities, and the unfolding progress on
arithmetic progressions -- along with some new results proved by me and my
collaborators. Hopefully I will have time to mention some nice research
problems as well.